PRECIOUS METALS IN SDSS QUASAR SPECTRA. II.
TRACKING THE EVOLUTION OF STRONG, 0.4 < z < 2.3 Mg
II ABSORBERS WITH THOUSANDS OF SYSTEMS
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Citation
Seyffert, Eduardo N., Kathy L. Cooksey, Robert A. Simcoe, John
M. O’Meara, Melodie M. Kao, and J. Xavier Prochaska.
“PRECIOUS METALS IN SDSS QUASAR SPECTRA. II.
TRACKING THE EVOLUTION OF STRONG, 0.4 < z < 2.3 Mg II
ABSORBERS WITH THOUSANDS OF SYSTEMS.” The
Astrophysical Journal 779, no. 2 (December 20, 2013): 161.
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http://dx.doi.org/10.1088/0004-637x/779/2/161
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Draft 5: January 20, 2014
Preprint typeset using LATEX style emulateapj v. 08/22/09
PRECIOUS METALS IN SDSS QUASAR SPECTRA II: TRACKING THE EVOLUTION OF STRONG,
0.4 < Z < 2.3 MG II ABSORBERS WITH THOUSANDS OF SYSTEMS
Eduardo N. Seyffert1 , Kathy L. Cooksey2,6 , Robert A. Simcoe1 , John M. O’Meara3 , Melodie M. Kao4 , and J.
Xavier Prochaska5
arXiv:1308.5971v2 [astro-ph.CO] 16 Jan 2014
Draft 5: January 20, 2014
ABSTRACT
We have performed an analysis of over 34,000 Mg II doublets at 0.36 < z < 2.29 in Sloan Digital
Sky Survey (SDSS) Data-Release 7 quasar spectra; the catalog, advanced data products, and tools
for analysis are publicly available. The catalog was divided into 14 small redshift bins with roughly
2500 doublets in each, and from Monte-Carlo simulations, we estimate 50% completeness at rest
equivalent width Wr ≈ 0.8 Å. The equivalent-width frequency distribution is described well by an
exponential model at all redshifts, and the distribution becomes flatter with increasing redshift, i.e.,
there are more strong systems relative to weak ones. Direct comparison with previous SDSS Mg II
surveys reveal that we recover at least 70% of the doublets in these other catalogs, in addition to
detecting thousands of new systems. We discuss how these surveys come by their different results,
which qualitatively agree but, due to the very small uncertainties, differ by a statistically significant
amount. The estimated physical cross-section of Mg II-absorbing galaxy halos increased three-fold,
approximately, from z = 0.4 → 2.3, while the Wr ≥ 1 Å absorber line density grew, dNMg II /dX, by
roughly 45%. Finally, we explore the different evolution of various absorber populations—damped
Lyman-α absorbers, Lyman-limit systems, strong C IV absorbers, and strong and weaker Mg II
systems—across cosmic time (0 < z < 6).
Subject headings: intergalactic medium – quasars: absorption lines – galaxies: halos — techniques:
spectroscopic
Online-only material: color figures, machine-readable tables
1. INTRODUCTION
The cosmic enrichment cycle describes the movement of gas and heavy elements (or metals) from
the sites of star formation in galaxies into the intergalactic medium (IGM) and potentially back again.
An understanding of gas surrounding galaxies—or the
circum-galactic medium (CGM)—is crucial to understanding feedback and gas accretion processes. Mg II
λλ2796, 2803 absorption-line surveys—in both quasar
and galaxy spectra—have long been utilized to characterize enriched, photoionized gas clouds within and surrounding galaxies (e.g., Bergeron 1986; Lanzetta et al.
1987; Sargent et al. 1988; Petitjean & Bergeron 1990;
Steidel & Sargent 1992; Churchill et al. 1999; Weiner
et al. 2009; Martin & Bouché 2009; Bordoloi et al. 2011;
Lovegrove & Simcoe 2011; Kacprzak et al. 2011a; Kornei
et al. 2012; Churchill et al. 2013; Rubin et al. 2013).
Mg II is a strong transition for a wide range of ionization parameters,7 even with a modest number of Mg
1 Department of Physics, MIT, 77 Massachusetts Avenue,
37-664D, Cambridge, MA 02139, USA; enseyff@mit.edu; simcoe@space.mit.edu
2 MIT Kavli Institute for Astrophysics & Space Research, 77
Massachusetts Avenue, 37-685, Cambridge, MA 02139, USA;
kcooksey@space.mit.edu
3 Department of Chemistry and Physics, Saint Michael’s College,
One Winooski Park, Colchester, VT 05439; jomeara@smcvt.edu
4 Caltech,
MC 249-17, 1200 East California Boulevard,
Pasadena, CA 91125; mkao@caltech.edu
5 Department of Astronomy & UCO/Lick Observatory, University of California, 1156 High Street, Santa Cruz, CA 95064, USA;
xavier@ucolick.org
6 NSF Astronomy & Astrophysics Postdoctoral Fellow
7 The ionization parameter, U , is the ratio of the number of
atoms, making it a common and well-studied ion. The
metallicities of Mg II systems, at 0.4 < z < 1.8, range
from one-tenth to super-solar (Rigby et al. 2002; Charlton et al. 2003; Misawa et al. 2008). Ground-based, optical spectrographs can detect the Mg II doublet over
0.1 . z . 2.5; infrared spectroscopy can extend that
range to z ≈ 5.5. Mg II absorption-line surveys take on
three flavors: (i) galaxy self-absorption; (ii) galaxies or
quasars probing galaxies; and (iii) quasar absorption-line
(QAL) spectroscopy. Results from all experimental setups provide evidence that Mg II absorption traces the
CGM, though only the first two methods identify the
host galaxies explicitly.
Strong Mg II absorbers, with rest equivalent widths
of the 2796 Å line Wr,2796 & 1 Å, have been linked to
massive, star-forming galaxies, possibly arising in their
starburst-driven outflows (Bouché et al. 2006; Weiner
et al. 2009; Rubin et al. 2010). In this model, Mg II
absorption is found in cool, interlaced clumps within a
heated galactic outflow. Recent results show that the
strength of the Mg II absorption depends on the azimuthal angle relative to the host galaxies (Bordoloi et al.
2011; Bouché et al. 2012; Kacprzak et al. 2012). Under
the model of a biconical starburst-driven outflow, the
stronger Mg II absorbers are detected over the plane of
the disk. Both studies detect weak Mg II absorption
at large azimuthal angles (i.e., along the disk axis), and
these systems may trace inflowing material (Chen et al.
2010b), possibly co-rotating with the disk (Kacprzak
et al. 2011b).
H-ionizing photons to the number of H atoms.
Seyffert et al.
8 Lundgren et al. (2009) conducted a completely automated
Mg II survey in a sub-sample of DR5 quasar spectra, in order to
conduct a Mg II-galaxy clustering analysis. We exclude comparison to this targeted QAL survey; however, ZM13 compare with
the Lundgren et al. (2009) results.
2012, ZM13). Though QAL surveys do not produce direct ties between Mg II absorbers and galaxies, the seemingly related evolution of dNMg II /dz for Wr,2796 ≥ 1 Å
and ρ∗ is at least circumstantial evidence that strong
Mg II systems are linked to star formation. Also, Ménard
et al. (2011) detected [O II] λ3727 nebular emission in
the SDSS fibers with Mg II absorption, which directly
ties the absorption to star formation.
Matejek & Simcoe (2012) observed little evolution in
dNMg II /dz for 0.3 Å ≤ Wr,2796 < 1 Å systems over 0.4 .
z2796 . 5.5, comparing to N05 and later upheld by ZM13.
This suggests a population of weak Mg II absorbers being
established early in the history of the universe or being
constantly replenished, at a conserving rate, over time.
In spite of the numerous observations of Mg II absorbers and their direct or inferred relationship with
galaxies, the origin of the absorbing gas in the CGM is
not yet clearly understood. We are motivated to conduct
a SDSS Mg II survey so that we may fairly compare the
results with our high-redshift results (Matejek & Simcoe
2012) and with our other SDSS metal-line surveys. We
have completed the search for C IV λλ1548, 1550 (Cooksey et al. 2013, hereafter, Paper I), and our survey of
Si IV λλ1393, 1402 is in preparation. We also discuss
why the various SDSS Mg II surveys produce different
results, which, due to the large sample sizes, are statistically significant.
We summarize how we construct our Mg II catalog,
correct for completeness, and compare with previous
SDSS catalogs in Section 2, while absorber-by-absorber
comparisons are left to Appendix A. The main results are
detailed in Section 3. We discuss the implications of our
results in the context of the CGM and the results from
surveys of other absorber populations in Section 4. The
summary is given in Section 5. We adopt the WMAP5
cosmology: H0 = 71.9 km s−1 Mpc−1 , ΩM = 0.258, and
ΩΛ = 0.742 (Komatsu et al. 2009).
80
1000
60
100
40
Number
Early-type galaxies also host Mg II systems (Chen
et al. 2010a; Gauthier et al. 2010; Gauthier & Chen
2011), and they tend to be weaker than absorbers around
star-forming galaxies (Bowen & Chelouche 2011), which
supports the idea that weak systems may trace gas accretion or at least the “ambient” CGM. Gauthier et al.
estimate the covering fraction of Mg II absorption to be
≈ 14% for massive luminous red galaxies and greater for
less massive galaxies. Chen et al. (2010a) searched for
absorbers in quasar sightlines near galaxies (as opposed
to seeking galaxies near sightlines with known Mg II
systems) and found no correlation to the star-formation
rate of the host galaxies. They traced the absorption in
bright, field galaxies out to about 100 kpc with 50–80%
covering fraction.
Gauthier (2013) propose that ultra-strong, Wr,2796 &
3 Å Mg II systems trace gas in galaxy groups (though
see Nestor et al. 2011). The ultra-strong Mg II absorbers
have broad, kinematically complex profiles. Galaxies in
groups may have different radial Wr,2796 profiles from
isolated galaxies (Chen et al. 2010a).
Mg II absorption has been used to select damped Lyα
absorber (DLA) candidates at z . 1.6, because it is a
common transition for even moderately metal-enriched
gas and can be observed with ground-based optical spectrographs (Rao & Turnshek 2000), whereas the distinctive Lyα profile is accessible only with space-based ultraviolet spectrographs. DLAs, with H I column densities
log NH I ≥ 20.3, are considered the cold gas reservoirs
for star formation and thought to reside in star-forming
galaxies (see Wolfe et al. 2005, and references therein).
The large database of quasar spectra generated by
SDSS (York et al. 2000) provides a way to efficiently
find strong Mg II systems in the range 0.4 < z < 2.3, or
from when the universe was 9.5 Gyr to 3 Gyr old. At
SDSS resolution (≈ 150 km s−1 ) and typical signal-tonoise, SDSS is more complete at Wr,2796 & 1 Å, defining
“strong” Mg II absorbers. There have been four SDSS
Mg II surveys in: the early data release or EDR—Nestor
et al. (2005, hereafter N05); DR3—Prochter et al. (2006a,
P06); DR4— Quider et al. (2011, Q11); and DR7— Zhu
& Ménard (2013, ZM13).8
Most of these studies measured the frequency distribution of Wr,2796 and the absorber redshift density,
dNMg II /dz. The former is fit well by an exponential model, showing that there is a break in the full
equivalent-width distribution, when accounting for the
weaker systems being well-modeled by a power-law distribution (Churchill et al. 1999; Narayanan et al. 2007).
For Wr,2796 ≥ 1 Å, dNMg II /dz increases by a factor of
≈ 2.5 from z ≈ 0.4 → 2.3. Recent results from an
infrared survey showed that dNMg II /dz decreases from
z ≈ 2 → 5.5 (Matejek & Simcoe 2012).
P06 first connected the Mg II evolution to the cosmic
star-formation rate density, ρ∗ , and Ménard et al. (2011)
constructed an empirical relation between dNMg II /dz
and ρ∗ , which peaks at z ≈ 2 to 3 and roughly
matches the dNMg II /dz evolution (Matejek & Simcoe
⟨S/N⟩ (pixel−1)
2
10
20
1
1
2
3
4
5
zQSO
Figure 1. Redshift and hS/Ni distribution of sightlines. Using
the left-hand axis, the 2D histogram shows the median signal-tonoise and zQSO space of the analyzed 79,294 spectra. The black
and gray histograms give the redshift distribution for all spectra
and for the 28,938 with confirmed Mg II absorbers, respectively
(right-hand axis).
Evolution of Strong Mg II Absorbers
3
Table 1
Sightline Summary
(1)
QSO ID
(2)
R.A.
(3)
Decl.
(4)
zQSO
52203-0685-467
52203-0685-470
52235-0750-082
52143-0650-199
52235-0750-499
51791-0387-200
52235-0750-098
52203-0685-198
52203-0685-439
52991-1489-142
52143-0650-459
00:00:06.53
00:00:08.13
00:00:09.38
00:00:09.42
00:00:11.41
00:00:11.96
00:00:13.14
00:00:14.82
00:00:15.47
00:00:16.43
00:00:17.38
+00:30:55.2
+00:16:34.6
+13:56:18.4
–10:27:51.9
+14:55:45.6
+00:02:25.3
+14:10:34.6
–01:10:30.7
+00:52:46.8
–00:18:33.3
–08:51:23.7
1.8246
1.8373
2.2342
1.8449
0.4597
0.4789
0.9582
1.8877
1.8516
0.7030
1.2491
(5)
hS/Ni
(pixel−1 )
7.85
10.34
4.17
8.54
7.83
11.16
12.26
9.21
7.22
6.20
7.44
(6)
fBAL
(7)
∆Xmax
(8)
Ncand
(9)
NMg II
(10)
δXMg II
0
0
0
0
0
0
0
0
0
0
0
4.04
2.27
0.19
3.33
0.49
1.64
2.15
2.87
2.47
0.92
3.74
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
···
···
···
0.028
···
···
···
···
···
···
···
Note. — Column 1 is the adopted QSO identifier from the spectroscopic modified Julian date, plate, and fiber
number. Columns 2 through 4 are from the DR7 QSO catalog (Schneider et al. 2010). Column 5 is the median S/N
measured in the region searched for Mg II. The binary BAL flag fBAL in Column 6 indicates which sightlines were
considered BALs by at least one author (4) and which were confirmed by the authors as BALs to exclude (8). Column
7 is the maximum co-moving pathlength available in the sightline. Columns 8 and 9 give the number of candidate and
confirmed Mg II doublets, respectively. Column 10 is the pathlength blocked by the NMg II doublets in the sightline.
(This table is available in a machine-readable form in the online journal. A portion is shown here for guidance regarding
its form and content.)
2. CONSTRUCTING THE MG II CATALOG
2.1. From Quasar Spectra to Visually Verified Sample
Our Mg II absorber catalog was constructed using a
subset of the SDSS DR7 quasar catalog (Schneider et al.
2010) and following an equivalent methodology to the
C IV survey described in detail in Paper I, to which the
interested reader is referred. Here we briefly outline the
procedure.
Of the 105,783 DR7 quasar spectra, 79,595 were
searched for Mg II systems (Table 1) because they: (i)
were not broad absorption-line (BAL) QSOs (identified
by Shen et al. 2011) and (ii) had median signal-to-noise
ratio hS/Ni ≥ 4 pixel−1 in the region covering intergalactic Mg II absorption (i.e., observed wavelengths greater
than 1250 Å(1 + zQSO ) and δvQSO < −3000 km s−1 ).9
A further 301 sightlines were later excluded as “visual”
BAL QSOs, leaving a total of 79,294 quasar spectra included in this survey; their distribution in zQSO –hS/Ni
space is shown in Figure 1.
Every quasar spectrum was normalized with its “hybrid continuum,” a fit combining principle-component
analysis, b-spline correction, and pixel/absorption-line
rejection. Absorption-line candidates were automatically
detected by convolving the normalized flux and error arrays with a Gaussian kernel with a full-width at halfmaximum of one pixel, roughly an SDSS resolution element (resel). Candidate Mg II doublets were identified based solely on the characteristic velocity separation
(767 km s−1 ), plus/minus 150 km s−1 to allow for blending. The candidate doublets had convolved (S/N)conv ≥
3.5 resel−1 in the 2796 Å line and 2.5 resel−1 in the 2803 Å
line. Any automatically detected absorption feature with
(S/N)conv ≥ 3.5 resel−1 and broad enough to enclose a
Mg II doublet was included in the candidate list.
The wavelength bounds of the absorption lines were
automatically defined by where the convolved S/N array
began increasing when stepping away from the automat9
Velocity offset is defined as δvQSO = c(z2796 − zQSO )/(1 +
zQSO ).
ically detected line centroid. The new centroid was then
set as the flux-weighted average wavelength within the
bounds, and the Mg II doublet redshift, z2796 , was defined by the new 2796 Å centroid.
From simulations of synthetic Mg II profiles with
known equivalent widths, we empirically determined that
capping the flux at the continuum plus one sigma (Poisson uncertainty of the flux and continuum error) yielded
the most accurate Wr measurements using the technique
of boxcar summation; the measured Wr was 0.08 Å larger
than the input Wr (in the median), with a median absolute deviation of 0.21 Å. Hence, our (observed) equivalent widths are the sum of this modified absorption
within the wavelength bounds (i.e., (1 − f )δλ).
All candidates were visually inspected by at least one
author and most by two. They were rated on a four-point
scale from 0 (definitely false) to 3 (definitely true). The
systems were judged largely on the Mg II doublet (e.g.,
centroid alignment, correlated profiles) but possibly associated ions were also reviewed to aid verification. All
Mg II absorbers with rating of 2 or 3 were included in
subsequent analyses and combined into systems if separated by less than 250 km s−1 .
Ultimately, we detected 35,629 doublets—from over
90,000 candidates—with Wr,2796 < 9 Å and 0.36 <
z2796 < 2.29 (Table 2). We excluded the C IV emissionline region, ±3000 km s−1 around 1548.195 Å(1 + zQSO ),
because the continuum fits in this region were questionable, owing to the potentially large velocity offsets of the
emission lines and the large incidence of strong intrinsic
absorption. In addition, real intervening Mg II absorption could be lost in the intrinsic C IV absorption, thus
hindering the recovery of Mg II systems in this region.
This reduced the total sample size by 531. We also limit
our sample to systems with δvQSO < −5000 km s−1 , leaving 34,254 doublets for further analyses.
2.2. Testing and Correcting for Completeness
As in Paper I, we test our survey completeness with
Monte-Carlo simulations. Ultimately, our complete-
4
Seyffert et al.
Table 2
Mg II System Summary
(1)
QSO ID
(2)
zQSO
(3)
z2796
(4)
Wr,2796
(Å)
(5)
Wr,2803
(Å)
(6)
C(Wr,2796 )
52235-0750-082
2.2342
52143-0650-199
1.8449
52203-0685-439
1.8516
52143-0650-459
54389-2822-318
51791-0387-167
51791-0387-531
54389-2822-339
1.2491
1.1560
2.1249
0.9511
1.4446
52143-0650-178
2.6404
52251-0751-355
51791-0387-093
1.4115
1.8973
0.96363
1.14500
1.31252
1.52824
1.37148
1.63660
0.69284
0.48941
1.07105
0.49645
0.38268
0.76378
1.09345
1.05622
1.38095
0.89761
1.02077
2.445 ± 0.174
0.268 ± 0.115
1.965 ± 0.235
0.394 ± 0.159
0.650 ± 0.212
1.457 ± 0.577
0.575 ± 0.162
2.724 ± 0.384
0.801 ± 0.256
0.310 ± 0.115
1.006 ± 0.555
2.117 ± 0.309
0.852 ± 0.387
1.749 ± 0.141
0.793 ± 0.113
1.749 ± 0.297
0.723 ± 0.172
1.547 ± 0.168
0.254 ± 0.143
2.016 ± 0.198
0.507 ± 0.180
1.140 ± 0.253
2.376 ± 0.396
0.486 ± 0.164
2.534 ± 0.375
0.631 ± 0.240
0.678 ± 0.132
1.684 ± 0.564
1.581 ± 0.304
1.036 ± 0.406
1.283 ± 0.172
0.619 ± 0.116
1.799 ± 0.290
0.791 ± 0.214
0.915 ± 0.006
0.112 ± 0.069
0.882 ± 0.034
0.203 ± 0.113
0.400 ± 0.163
0.789 ± 0.249
0.344 ± 0.126
0.924 ± 0.012
0.495 ± 0.174
0.142 ± 0.074
0.600 ± 0.352
0.898 ± 0.038
0.526 ± 0.268
0.851 ± 0.025
0.490 ± 0.071
0.852 ± 0.064
0.446 ± 0.120
Note. — For each sightline (identified in Columns 1 and 2), every confirmed doublet is
listed by the redshift of its Mg II 2796 line (Column 3). The rest equivalent widths of the
Mg II lines are given in Columns 4 and 5. In Column 6, we give the completeness fraction
for the doublet from the whole survey average. (This table is available in a machinereadable form in the online journal. A portion is shown here for guidance regarding its
form and content.)
0.25
Accepted Spurious Fraction
Cuser(z2795 or ⟨S/N⟩)
1.0
0.9
0.8
0.7
0.6
0.5
1.0
1.5
2.0
10
20
⟨S/N⟩ (pixel−1)
z2795
30
0.10
0.05
40
0.5
1.0
1.5
2.0
10
20
⟨S/N⟩ (pixel−1)
z2795
30
40
0.25
0.8
0.6
0.4
0.2
z2795 < 0.63
z2795 ≥ 1.78
0.63 ≤ z2795 < 1.78
0.5
1.0
Wr,2795 (Å)
1.5
0.0
0.5
1.0
Wr,2795 (Å)
1.5
Accepted Spurious Fraction
1.0
Cuser(Wr,2795)
0.15
0.00
0.5
0.0
0.0
0.20
0.20
0.15
0.10
0.05
0.00
0.0
z2795 < 0.63
z2795 ≥ 1.78
0.63 ≤ z2795 < 1.78
0.5
1.0
Wr,2795 (Å)
1.5
0.0
0.5
1.0
Wr,2795 (Å)
1.5
Figure 2. Biases of visual verification and trends of spurious detections. Left: We tested the “user bias” by rating fake λλ2795, 2801
doublets that were injected and automatically recovered as candidates. The four panels show the completeness of our ability to correctly
rate true doublets, as a function of redshift, spectrum hS/Ni, and equivalent width in three redshift bins. The redshift cuts (vertical lines)
were determined by changes in Cuser (z2795 ) and to align with the closest redshift bins used in our analyses. The solid and dashed lines
are the best-fit model, Cuser (Wr ) = C0 (1 − exp(β(Wr − W0 ))), and its 1-σ errors. Right: We plot the accepted false-positive fraction as
functions of redshift, signal-to-noise, and equivalent width. These spurious pairs of lines were not injected but were automatically recovered.
The lower panels show the best-fit model and errors to the accepted spurious fraction over Wr,2795 .
ness fractions, C(z, W ), are the ratios of the number
of accepted (i.e., visually verified), simulated doublets,
Naccept , to the number input, Ninput , as a function of
z2796 and Wr,2796 . We estimate C(z, W ) in four steps,
described below.
First, in a “basic” completeness test, we measured the
number, Nrec , of simulated Mg II doublets recovered
by our automated procedures, from continuum fitting
to candidate selection. We generated a library of synthetic profiles, inserted them into a representative subset
of sightlines, and tracked which profiles were automatically recovered. The simulated doublets reflected the ob-
served variety in our SDSS Mg II catalog. By construction, they uniformly spanned 0.05 Å ≤ Wr,2796 < 6.5 Å
but ≈ 20% sampled 6.5 Å–8 Å with decreasing frequency.
We injected 1000 simulated doublets in 30% of the sightlines at a rate of dN /dz = 5. The tested sightlines sampled the entire zQSO –hS/Ni space, and the un-sampled
sightlines were assigned the mean completeness fraction
of the tested sample in small bins of zQSO and hS/Ni.
Second, we estimated the “user” bias, resulting from
our visual verification. We determined the rate at which
we accepted real doublets (“true positives”) and spurious
Evolution of Strong Mg II Absorbers
pairs (“accepted false positives”); the latter are chance
alignments and/or noise fluctuations. As in Paper I, we
injected simulated fake doublets, with rest wavelength
comparable to Mg II but with characteristic separation
of 652 km s−1 , and visually rated the recovered candidates, thus measuring the accepted number, Naccept . Effectively, the completeness fraction is now:
C(z, W ) =
Nrec (z, W ) Naccept (z, W )
.
Ninput (z, W ) Nrec (z, W )
(1)
However, as in Paper I, we fitted a functional form to
the accepted-to-recovered fraction, Cuser (z, W ) = C0 (1−
exp(β(Wr − W0 ))). This adjustment slightly increased
the total completeness fraction measured in the “basic”
test.
We injected Ninput = 16, 209 fake doublets with Wr <
2 Å and δvQSO < −5000 km s−1 , and Nrec = 10, 258
were automatically recovered. Of these, we correctly
rated Naccept = 8472. The automatically generated candidate list included any pair of lines with separations
within ±150 km s−1 (see Section 2.1) of the fake doublet separation, which brought forth true fake doublets,
real Mg II systems, and common contaminants. These
contaminating pairs of lines intrinsically had a range
of separations—fixed, if they are from the same system, or random, if a pair of spurious lines. Thus the
652 ± 150 km s−1 search window was sampled by a distribution very representative of contaminants affecting the
Mg II survey.
As shown in Figure 2 (left panels), the user completeness generally decreases with increasing redshift and decreasing spectrum hS/Ni and Wr . We divide the Cuser
fit at z = 0.63 and z = 1.78, where Cuser changes rapidly
and which align with our fixed bins.
Third, we scaled the completeness by the fraction of
the total co-moving path length10 not blocked by doublets with greater Wr in the given redshift bin. All Mg II
lines blocked less than 1% of the total survey path length
(Table 2). This correction slightly decreased the total
completeness fraction. To measure the unblocked comoving path length available in our survey, we multiply
C(W ) by the total path available in the given redshift
bin (Figure 3).
Fourth, the user completeness tests enabled measurement of the accepted false-positive rate, dNafp /dX.
There were 5802 spurious candidates from the automated
search, of which we incorrectly accepted 678. As shown
in Figure 2 (right panels), the accepted false-positive
fraction is roughly constant at ≈ 10% as a function
of redshift and signal-to-noise. However, the fraction
increases with increasing Wr , plateauing to ≈ 10% at
z < 1.78 and ≈ 20% at higher redshift. For Wr ≥ 1 Å,
we estimate dNafp /dX = 0.0015 (z < 0.63), 0.0020
(0.63 ≤ z < 1.78), and 0.0045 (z ≥ 1.78). We explain
how we adjust for the accepted false-positive rate in Section 3.
As mentioned previously,
we excluded the
±3000 km s−1 around the quasar C IV emission line.
This reduced the pathlength by 7% over 1.48 ≤ z < 1.78
and less (2%–5%) in other noticeably affected bins,
1.20 ≤ z < 2.29.
2.3. Comparing with Previous SDSS Mg II Catalogs
There have been four Mg II surveys using different
SDSS data releases: early (Nestor et al. 2005); third
(Prochter et al. 2006a); fourth (Quider et al. 2011); and
seventh (Zhu & Ménard 2013).11 The surveys have a
variety of differences that contribute to variations between line lists for the same subset of quasars and, hence,
the results (e.g., dNMg II /dX), which we discuss in Section 3. Here we summarize the differences in catalogs
and methodologies—from continuum fitting to final doublet selection; we leave the detailed absorber-to-absorber
comparisons to Appendix A.
N05 and Q11 model the intrinsic quasar spectra with
a combination of cubic splines and Gaussian profiles for
emission lines, while P06 use b-splines and principlecomponent analysis (PCA) for emission lines. ZM13 and
this study use PCA for both continua and emission lines
and correct for low-frequency modulations automatically
in post-processing.
All catalogs are visually verified, except for ZM13. The
latter uses the Q11 catalog as their training set, and Q11,
in turn, is based on the methodologies of N05. These
three studies model the absorption lines with a (single
or double) Gaussian profile, from which they measure
the equivalent widths. These three studies and our work
agree well on Wr,2796 values.
Our automated candidate doublet search is based on
the algorithm used by P06. We both use boxcar summation to measure equivalent widths, but P06 fix the box
width, while we let it vary automatically depending on
the profile. The fixed width contributes to the disagreement in our equivalent-width measurements, with P06
underestimating Wr,2796 . More importantly, the continuum placement in P06 was biased low by the strong absorption systems, systematically reducing their equivalent widths.
All surveys estimate their sample completeness, and
all but Q11 use Monte-Carlo simulations in a similar
fashion to ours, though number of realizations, types of
profiles, etc. differ. Q11 relied on the tests of the automated algorithms that N05 conducted and assessed their
false-negative rate by having two authors visually verify
a small number of sightlines. Q11 focused on describing
their catalog, and any analyses did not rely on correcting
for completeness.
To summarize, the detailed catalog-to-catalog comparisons (Appendix A), we recover over 76% of the P06 absorbers, 80% of Q11, and 72% of ZM13.12 We can also
identify why we do not recover the remaining doublets,
with reasons ranging from the Shen et al. (2011) BAL
QSO spectra were not searched to the line was not automatically detected by our algorithms in our normalized
spectra. All catalogs are less complete for weaker systems, and each catalog’s unmatched sample largely has
Wr,2796 . 1 Å.
Statistically and intuitively, disagreement at low
equivalent width—where all surveys become highly
11
10
The co-moving
p path length is related to redshift as follows:
dX/dz = (1 + z)2 / ΩM (1 + z)3 + ΩΛ .
5
See footnote 8.
N05 did not publish their line list so detailed comparison is
not possible.
12
6
Seyffert et al.
2.5•104
∆X(Wr,2796)
2.0•104
0.36 ≤ z < 0.52
NLOS = 71178; ∆Xmax = 17037
W50% = 1.04 Å
0.52 ≤ z < 0.63
NLOS = 69257; ∆Xmax = 13739
W50% = 0.82 Å
0.63 ≤ z < 0.73
NLOS = 66862; ∆Xmax = 13048
W50% = 0.74 Å
0.73 ≤ z < 0.82
NLOS = 65161; ∆Xmax = 12058
W50% = 0.72 Å
0.82 ≤ z < 0.91
NLOS = 63433; ∆Xmax = 12320
W50% = 0.71 Å
0.91 ≤ z < 1.00
NLOS = 61100; ∆Xmax = 11944
W50% = 0.80 Å
1.00 ≤ z < 1.11
NLOS = 58208; ∆Xmax = 14924
W50% = 0.93 Å
1.11 ≤ z < 1.20
NLOS = 53896; ∆Xmax = 11850
W50% = 0.76 Å
1.20 ≤ z < 1.30
NLOS = 50016; ∆Xmax = 11904
W50% = 0.70 Å
1.30 ≤ z < 1.39
NLOS = 45564; ∆Xmax = 10177
W50% = 0.53 Å
1.39 ≤ z < 1.49
NLOS = 41489; ∆Xmax = 10394
W50% = 0.58 Å
1.49 ≤ z < 1.60
NLOS = 36574; ∆Xmax = 10060
W50% = 0.63 Å
1.60 ≤ z < 1.78
NLOS = 31247; ∆Xmax = 13671
W50% = 0.82 Å
1.78 ≤ z < 2.29
NLOS = 23124; ∆Xmax = 11545.8×2
W50% = 1.22 Å
0.36 ≤ z < 2.29
NLOS = 79111; ∆Xmax = 15256.0×12
W50% = 0.81 Å
1.5•104
1.0•104
5.0•103
2.5•104
∆X(Wr,2796)
2.0•104
1.5•104
1.0•104
5.0•103
2.5•104
∆X(Wr,2796)
2.0•104
1.5•104
1.0•104
5.0•103
2.5•104
∆X(Wr,2796)
2.0•104
1.5•104
1.0•104
5.0•103
1
2
3
Wr,2796 (Å)
4
5
1
2
3
Wr,2796 (Å)
4
5
1
2
3
Wr,2796 (Å)
4
5
Figure 3. Results from Monte-Carlo completeness tests. The completeness-corrected co-moving path length as a function of rest equivalent
width, ∆X(Wr,2796 ), is shown for the 15 redshift bins used in the current study. The black lines and errors are the completeness curves,
and the gray points and errors are the observations. The horizontal, dashed line traces the maximum path length available in the bin, and
the vertical, dotted line indicates the equivalent width where we are 50% complete.
incomplete—is expected. For example, we are 50% complete at Wr,2796 ≈ 0.8 Å, while ZM13 is roughly 60%
complete, so we should only agree on ≈ 30% of doublets
of this strength. There is a large caveat because we all use
SDSS spectra: our surveys are not statistically independent. However, continuum placement factors strongly
into the automated detection of weak lines, which is why
we attempt to quantify this affect by refitting the continua in our Monte-Carlo completeness tests.
In all cases, we detect Mg II systems not in other catalogs. Since P06 applied a hard Wr,2796 ≥ 1 Å cut, the
vast majority of our unique systems are at lower equivalent widths, but their redshift distribution typically follows the full sample. The P06-only sample favors higher
redshifts where sky lines are abundant and make verification difficult.
The redshifts of the Q11- and ZM13-only samples are
a fair sampling of the full (parent) samples. However,
our unique sample favors lower redshift. The effect is
more pronounced with respect to ZM13, which limited
the search to ∆z ≥ 0.02 red-ward of the quasar C IV
emission line.
Another point of comparison is the Wr,2796 /Wr,2803 ratio. For the matched samples, we tend to measure larger
ratios than Q11 and significantly larger than ZM13; P06
did not publish Wr,2803 measurements. Our unique sample has a significant number of systems with ratios less
than unity, indicating we identify more blended systems.
In Section 3, we compare our science results with the
published catalogs, where such comparisons are suitable.
3. RESULTS
Typically, we analyzed our Mg II catalog as a whole
and in 14 small redshift bins with roughly 2500 doublets
each. As necessary, we modify the redshift binning to
match other samples when comparing to their results.
3.1. Frequency Distribution
The equivalent-width frequency distribution f (Wr )
(sometimes written, d2 NMg II /dWr /dX) is the number of
detections Nobs (Wr ) per rest equivalent width bin ∆Wr ,
per the total co-moving path length available, in the
given equivalent-width bin, ∆X(Wr ):
f (Wr ) =
Nobs (Wr )
,
∆Wr ∆X(Wr )
(2)
and it is ∆X(Wr ) that accounts for completeness.
We modeled f (Wr ) with an exponential, f (Wr ) =
Evolution of Strong Mg II Absorbers
log f(Wr,2796)
0
7
0.36 ≤ z < 0.52
NMgII = 2414; W50% = 1.04 Å
0.52 ≤ z < 0.63
NMgII = 2402; W50% = 0.82 Å
0.63 ≤ z < 0.73
NMgII = 2491; W50% = 0.74 Å
0.73 ≤ z < 0.82
NMgII = 2445; W50% = 0.72 Å
0.82 ≤ z < 0.91
NMgII = 2575; W50% = 0.71 Å
0.91 ≤ z < 1.00
NMgII = 2288; W50% = 0.80 Å
1.00 ≤ z < 1.11
NMgII = 2557; W50% = 0.93 Å
1.11 ≤ z < 1.20
NMgII = 2356; W50% = 0.76 Å
1.20 ≤ z < 1.30
NMgII = 2521; W50% = 0.70 Å
1.30 ≤ z < 1.39
NMgII = 2515; W50% = 0.53 Å
1.39 ≤ z < 1.49
NMgII = 2431; W50% = 0.58 Å
1.49 ≤ z < 1.60
NMgII = 2321; W50% = 0.63 Å
1.60 ≤ z < 1.78
NMgII = 2467; W50% = 0.82 Å
1.78 ≤ z < 2.29
NMgII = 2471; W50% = 1.22 Å
0.36 ≤ z < 2.29
NMgII = 34254; W50% = 0.81 Å
−1
−2
−3
−4
log f(Wr,2796)
0
−1
−2
−3
−4
log f(Wr,2796)
0
−1
−2
−3
−4
log f(Wr,2796)
0
−1
−2
−3
−4
1
2
3
4
Wr,2796 (Å)
5
6
1
2
3
4
Wr,2796 (Å)
5
6
1
2
3
4
Wr,2796 (Å)
5
6
Figure 4. Equivalent-width frequency distributions. The maximum likelihood fits of an exponential function are the dashed (red) lines,
for each redshift bin, and the solid (gray) line, for the full sample. There is distinct evolution with redshift: f (Wr ) flattens (larger fraction
of strong absorbers) and increases (more absorbers overall) with increasing redshift. The observations have been completeness corrected,
and the redshift-specific 50% completeness limits are the vertical dotted lines.
k exp(αWr ), and fitted with the maximum likelihood
method of Cooksey et al. (2010) for Wr,2796 ≥ 0.8 Å,
though the results are relatively insensitive to a change
of ±0.2 Å. The exponential model is a very good description of the data (Figure 4), and the best-fit parameters
are given in Table 3.
The frequency distribution flattens with increasing redshift, meaning there are more strong absorbers relative
to weak ones, from z2796 = 0.4 → 2.3. The relatively
smooth and significant evolution in the best-fit parameters from low-to-intermediate redshift can be seen in
Figure 5. We also show that the line density is lower at
the extrema of the redshift range, where:
dNMg II −k αWlim
=
e
,
(3)
dX fit
α
from the integral of the frequency distribution from a
limiting equivalent width, Wlim , to infinity.
For Mg II, the normalization (k) increases by a factor of
≈ 2.5 from z = 2.3 → 0.4, while the scale (α) decreases by
approximately 20%. In comparison, for C IV, α evolves
little from z = 4.5 → 1.5, while k increases by three-fold,
roughly (Paper I).
As in Paper I, we factor in the accepted false-positive
rate by scaling the original, measured frequency distribution, f0 (Wr ):
dNafp /dX
f (Wr ) = 1 −
f0 (Wr ),
(4)
dNMg II /dX
which results in an updated best-fit normalization of:
dNafp /dX
k = 1−
k0 .
(5)
(dNMg II /dX)fit
In the latter equation, the denominator uses the integrated line density from Equation 3. We report the propagated errors in Table 3 and in the text.
From high-resolution, high-S/N spectroscopy of a
smaller number of quasars, Churchill et al. (1999) and
Narayanan et al. (2007) both measure a power-law
f (Wr ) for Wr,2796 . 0.3 Å systems. SDSS—as an efficient, low-resolution, moderate-S/N survey—naturally
provides great statistics on the rare, strong systems typically missing in smaller surveys. In Paper I, the newly
measured strong-end of the C IV frequency distribution
was also well-modeled by an exponential, which provided the first detection of a break, since previous (high-
Seyffert et al.
−1.0
0.13
0.15
MgII 0.36−2.29
1) 0.36−0.52
2) 0.52−0.63
3) 0.63−0.73
4) 0.73−0.82
5) 0.82−0.91
6) 0.91−1.00
7) 1.00−1.11
8) 1.11−1.20
9) 1.20−1.30
10) 1.30−1.39
11) 1.39−1.49
12) 1.49−1.60
13) 1.60−1.78
14) 1.78−2.29
0.11
14
−1.2
0.09
13
Scale α (Å−1)
12
11
9
0.07
8
10
−1.4
7
3
5
4
6
−1.6
2
1
−1.8
0.4
0.6
0.8
Normalization k (Å−1)
1.0
Figure 5. Best-fit f (Wr ) parameters and errors. We fitted the
frequency distribution with an exponential function. The best-fit
normalization k and scale α and the 1-σ error ellipses are plotted for
the 14 small redshift bins (numbered points); the 1, 2, and 3-σ contours are shown for the fit to the full sample (black ellipses). The
best-fit parameters evolve fairly smoothly with redshift, as seen by
comparing the ellipses with the constant dNMg II /dX curves (gray,
dashed lines; see Equation 3).
resolution, high-S/N, smaller sample) studies had modeled the frequency distribution as a power-law.
3.2. Mg II Absorber Line Density
The absorber line density is the completeness-corrected
number of Mg II doublets within the given Wr,2796 limits, normalized by the total redshift or co-moving path
length available, i.e., dNMg II /dz or dNMg II /dX, respectively. We subtract the accepted false-positive line density, dNafp /dz or dNafp /dX, from our quoted Mg II line
densities, for the appropriate redshift bin (Figure 2). For
+0.0001
Wr ≥ 1 Å, dNafp /dX = 0.0021−0.0001
(0.3 < z < 2.3);
+0.0003
+0.0001
0.0015−0.0003 (z < 0.63); 0.0020−0.0001
(0.63 ≥ z <
1.78); and 0.0045+0.0011
(z
≥
1.78).
−0.0010
In Figure 6, we compare dNMg II /dX for a range of
limiting equivalent widths, Wr,lim . There is significant
differential evolution based on Wr,lim , as predicted by
the changing shape of f (Wr ) over time (Figure 4). The
Wr ≥ 1 Å absorbers increase by approximately 45% from
z = 0.4 → 1.5, while the Wr ≥ 2 Å systems increase by a
a factor of 2.3 in over the same interval.
The peak in dNMg II /dX appears to shift to higher redshift for larger Wr,lim , from z ≈ 1.5 (Wr ≥ 0.8 Å) to
z ≈ 1.7 (Wr ≥ 2 Å). The cosmic star-formation rate
density (ρ∗ ) peaks at 2 . z . 3 (Bouwens et al. 2010).
Observations have associated strong Mg II systems with
outflows from star-forming galaxies. It is reasonable that
there would be more strong systems closer to the peak
in ρ∗ . The changing shape of f (Wr ) supports this result.
Matejek & Simcoe (2012) showed that weaker, 0.3 Å ≤
Wr,2796 < 1 Å systems evolve surprisingly little from
z ≈ 5.5 → 0.4. This persistent, weaker Mg II population arises either from pre-enrichment at early times or
constant replenishment (at a density-preserving rate), for
most of the lifetime of the universe.
We note that the 50% completeness limit in our highest redshift bin is Wr,2796 ≈ 1.2 Å, significantly higher
than our other bins (due to poor skyline subtraction).
We extend our analysis in this bin to below this value
in order to compare to results using the canonical 1 Å
limit. As seen in Figure 6, dNMg II /dX does consistently
decrease for equivalent-width cuts greater than the 50%
completeness limit, so the turnover is likely real. We discuss the possible physical explanations for the observed
evolution in dNMg II /dX in Section 4.
Quasars are not the only background source suitable
for absorption-line studies; gamma-ray bursts (GRBs)
have also been used to study intergalactic Mg II absorption systems. In the seminal study on Mg II doublets in
GRB sightlines, Prochter et al. (2006b) identified roughly
four-times as many systems as would be expected based
on the P06 quasar dNMg II /dX measurement. The authors discussed possible explanations: high-velocity, intrinsic Mg II population in GRB hosts; bias due to dust
obscuration in quasar sightlines; GRBs having larger
cross-sections; and effects of gravitational lensing. However, subsequent studies never fully resolved the difference between GRB and QSO dNMg II /dX. Recently,
Cucchiara et al. (2013) tackled the issue by increasing
the GRB statistics—including a completely independent
sample from Prochter et al. (2006b). Using the ZM13
dNMg II /dX values, which, as seen in Figure 7, are larger
than P06, Cucchiara et al. (2013) concluded that there
is no statistical difference between GRB and QSO sightlines. The latest dNMg II /dz results from this work are
≈ 10%–20% larger than those from ZM13, which brings
the GRB and QSO results further in to agreement.
10 9
8
7
Age of Universe (Gyr)
6
5
4.5
4
0.25
dNMgII/dX (Wr,2796 ≥ Wr,lim)
8
3.5
3
Wr,2796 ≥ 0.60 Å
Wr,2796 ≥ 0.80 Å
Wr,2796 ≥ 1.00 Å
Wr,2796 ≥ 1.50 Å
Wr,2796 ≥ 2.00 Å
0.20
0.15
0.10
0.05
0.5
1.0
1.5
2.0
z2796
Figure 6. Mg II absorber line density evolution. The number of
absorbers per co-moving path length increases from z2796 = 0.4 →
≈ 1.6. As expected from the flattening of f (Wr ) towards higher
redshift (Figure 4), the stronger systems show more evolution, increasing in number towards higher redshift. We are typically 50%
complete at Wr ≈ 0.8 Å.
3.3. Comparing with Previous SDSS Mg II Results
Previous SDSS Mg II surveys typically fitted
f (Wr,2796 ) with an exponential model and measure
Evolution of Strong Mg II Absorbers
9
Table 3
Mg II Results Summary
(1)
hzi
(2)
zlim
(3)
Nobs
(4)
∆Xmax
(5)
W50%
(Å)
(6)
dNMg II /dz
(7)
dNMg II /dX
(8)
Nfit
(9)
k
(Å−1 )
(10)
α
(Å−1 )
(11)
χ2red
1.10749
0.45524
0.57586
0.68065
0.77562
0.86369
0.94890
1.04931
1.15652
1.25157
1.34541
1.43499
1.54058
1.67796
1.91822
[0.36539, 2.28259]
[0.36539, 0.51988]
[0.52003, 0.62992]
[0.63003, 0.72993]
[0.73005, 0.81998]
[0.82002, 0.90992]
[0.91002, 0.99998]
[1.00003, 1.10999]
[1.11001, 1.20000]
[1.20005, 1.29999]
[1.30009, 1.38999]
[1.39003, 1.48998]
[1.49024, 1.59994]
[1.60001, 1.77974]
[1.78010, 2.28259]
34254
2414
2402
2491
2445
2575
2288
2557
2356
2521
2515
2431
2321
2467
2471
183071
17037
13739
13048
12057
12320
11944
14924
11850
11904
10176
10394
10060
13671
23091
0.81
1.04
0.82
0.74
0.72
0.71
0.80
0.93
0.76
0.70
0.53
0.58
0.63
0.82
1.22
0.293+0.002
−0.002
0.162+0.004
−0.004
0.191+0.005
−0.005
0.220+0.006
−0.005
0.251+0.006
−0.006
0.274+0.007
−0.007
0.295+0.007
−0.007
0.292+0.006
−0.006
0.332+0.008
−0.008
0.330+0.008
−0.008
0.369+0.010
−0.009
0.374+0.010
−0.010
0.400+0.010
−0.010
0.398+0.009
−0.009
0.360+0.007
−0.007
0.123+0.001
−0.001
0.096+0.002
−0.002
0.102+0.003
−0.003
0.110+0.003
−0.003
0.118+0.003
−0.003
0.123+0.003
−0.003
0.126+0.003
−0.003
0.119+0.003
−0.003
0.130+0.003
−0.003
0.125+0.003
−0.003
0.135+0.004
−0.003
0.133+0.003
−0.003
0.138+0.004
−0.003
0.132+0.003
−0.003
0.111+0.002
−0.002
22414
1509
1485
1510
1508
1627
1480
1749
1590
1578
1550
1543
1527
1771
1987
0.71+0.02
−0.02
0.96+0.11
−0.10
0.87+0.10
−0.09
0.75+0.08
−0.08
0.83+0.09
−0.08
0.83+0.09
−0.08
0.86+0.10
−0.09
0.75+0.08
−0.07
0.67+0.07
−0.06
0.64+0.06
−0.06
0.72+0.07
−0.07
0.65+0.06
−0.06
0.64+0.06
−0.06
0.52+0.05
−0.04
0.42+0.04
−0.04
−1.40+0.01
−0.01
−1.73+0.06
−0.06
−1.63+0.06
−0.06
−1.51+0.06
−0.06
−1.54+0.06
−0.06
−1.50+0.05
−0.05
−1.51+0.06
−0.06
−1.44+0.05
−0.05
−1.35+0.05
−0.05
−1.32+0.05
−0.05
−1.36+0.05
−0.05
−1.31+0.05
−0.05
−1.27+0.05
−0.05
−1.19+0.04
−0.04
−1.16+0.04
−0.04
0.535
1.519
2.422
1.327
1.617
1.240
1.658
1.535
1.836
1.060
1.237
2.267
1.652
1.064
2.489
Note. — Summary of the most common redshift bins and data used for the various analyses. Columns 1–2 give the median,
minimum, and maximum redshifts for the observed number of doublets (Column 3), and the maximum co-moving pathlength in the
redshift bin is given in Column 4. The 50% completeness limit from the Monte Carlo tests is in Columns 5. The redshift and co-moving
absorber line densities for Wr ≥ 1.0 Å are in Columns 6–7. The frequency distribution was fit with an exponential f (Wr ) = k exp(αWr )
for Nfit absorbers with Wr ≥ 0.8 Å (Column 8), and the best-fit parameters are given in Columns 9–10. The reduced χ2 from the best
fit and f (Wr ) (in bins with ≈ 100 doublets each) is given in Column 11.
Age of Universe (Gyr)
3
2
6
1.3
Age of Universe (Gyr)
3
2
6
1.3
0.7
dNMgII/dz (Wr,2796 ≥ 1.0Å)
0.6
0.5
0.4
0.3
Seyffert et al. 2013
Nestor et al. 2005
Prochter et al. 2006a
Prochter et al. 2006b
Zhu & Menard 2013
Matejek & Simcoe 2012
0.20
dNMgII/dX (Wr,2796 ≥ 1.0Å)
Seyffert et al. 2013
Nestor et al. 2005
Prochter et al. 2006a
Prochter et al. 2006b
Zhu & Menard 2013
Matejek & Simcoe 2012
0.15
0.10
0.2
0.05
0.1
1
2
3
z2796
4
5
1
2
3
z2796
4
5
Figure 7. Redshift (left) and co-moving path length (right) Mg II line densities. We compare apples-to-apples dNMg II /dz with Wr ≥ 1 Å
from six surveys: this work (blue plusses); N05 (cyan crosses); P06 (light gray squares); Prochter et al. (2006b, dark gray squares); ZM13
(green diamonds); and Matejek & Simcoe (2012, red triangles). The redshift density steadily increases from z ≈ 0.4 to ≈ 1.75. The
relatively flat dNMg II /dX indicates modest evolution in the product of the co-moving number density and the physical cross-section of the
absorbing clouds.
dNMg II /dz as a function of redshift, and here we compare their results with ours. The biggest caveat when
comparing results is: all SDSS Mg II studies are statistically correlated, since they are based on subsets of
the same observations. In addition, there are dependencies between methodologies. Since ZM13 used Q11 as a
training set, and the latter, in turn, was based heavily
on the methodologies of N05, the results of these studies
are highly correlated.
All studies that fitted f (Wr ) (N05; ZM13) find it
well-modeled by an exponential, with no apparent
break over 0.3 Å . Wr,2796 . 10 Å. These studies fitted the frequency distribution as: f (Wr ) =
dNMg II /dWr /dz = N ∗ /W ∗ exp(−Wr /W ∗ ), which relates better to a Schechter function formalism. Relating
our fit parameters to this formalism yields: k = −N ∗ α
and α = −(W ∗ )−1 . N05 found that the characteristic
equivalent width, W ∗ , increased steadily in their three
redshift bins covering z = 0.4 → 2.3. Over their 12 redshift bins, ZM13 measured a turnover in W ∗ at z ≈ 1.75.
10
Seyffert et al.
Matejek & Simcoe (2012) measured a monotonically decreasing W ∗ from z = 2 → 5.5, which mapped well on to
the N05 values.
For comparison, we fit the frequency distribution in
redshift space and convert the best-fit parameters, k and
α, to the fairly comparable quantities, N ∗ and W ∗ . We
measure steadily increasing W ∗ with redshift, in agreement with N05.13 N05 detect no evolution in N ∗ over
z = 0.4 to 2.3 (three redshift bins). Matejek & Simcoe
(2012) also detect no evolution from z = 2 to 5.5 (also
three bins). However, the Matejek & Simcoe values are
about 50% larger than the N05 measurements, with no
obvious evolution in the total of six redshift bins to bring
this about. On the other hand, N ∗ as estimated by ZM13
steadily increases from z = 0.4 to 2.3, mapping well on
to the high-redshift values.
However, as shown in Figure 5, the fit parameters are
correlated: small increases in W ∗ (or decreases in α)
decreases N ∗ (increases k). The measured dNMg II /dz,
which is a well-measured quantity, basically defines the
error ellipse. Therefore, though N05 and our W ∗ values
evolve consistently on to the high-redshift measurements,
both our N ∗ values disagree with the high-redshift estimates. For us, this manifests as a turnover in N ∗ at
z ≈ 1.5, while the ZM13 values steadily increase.
We compare our Wr,2796 ≥ 1 Å dNMg II /dz and
dNMg II /dX values to the other studies in Figure 7.
We compiled dNMg II /dz from the literature as follows:
N05—Figure 9; Prochter et al. (2006b)—best-fit polynomial, updating P06;14 ZM13—Figure 13; and Matejek
& Simcoe (2012)—Table 5. As for dNMg II /dX, we use:
P06—Table 3 and Matejek & Simcoe (2012)—Table 5.
As needed, we convert one line density to the other using dz/dX or its inverse,15 computed at the appropriate
redshift.
For all studies, the redshift density steadily increases
from z ≈ 0.4 to at least z ≈ 1.8, and comparing to
the high-redshift values (Matejek & Simcoe 2012), there
appears to be a peak between z ≈ 1.5 and 3.
However, expansion of the universe contributes to the
evolution of dNMg II /dz. Thus, we turn to dNMg II /dX,
where the normalization by co-moving path length removes the effect of passive evolution. In Figure 7,
dNMg II /dX evolves less strongly. Examining just the
SDSS results, the peak appears to be between z ≈ 1.5
and 2. The z = 2 to 3 values from Matejek & Simcoe
(2012) are larger than the highest-redshift SDSS values
but consistent within the large uncertainties.
Now we discuss why the SDSS dNMg II /dX measurements, which are drawn from the same actual spectra,
differ by amounts ranging from ≈ 15% (i.e., ours relative
to ZM13) to ≈ 50% (relative to P06). Since the formal errors quoted by surveys (≈ 1%) are much smaller than the
differences, we conclude that the uncertainties are dominated by systematic effects explored below, in addition to
completeness corrections, which are not discussed. Two
systematic effects contribute to dNMg II /dX differences:
13
Since our highest redshift bin begins where ZM13 detect a
turnover, we fitted f (Wr ) in three bins matching theirs and still
detect a monotonically increasing W ∗ .
14 Prochter et al. (2006b) updated the P06 analysis, increasing
their Mg II line density by ≈ 20%.
15 See footnote 10 .
Malmquist bias and variations in Wr,2796 measurements.
The Malmquist bias refers to how more absorbers scatter
to above Wr,lim than scatter to below, due to the Wr uncertainties, for distributions steeply rising toward weak
absorbers.
Due to the exponential nature of f (Wr ), a small change
in Wr,lim can have significant impact on the quoted
dNMg II /dX (see Equation 3); also, systematic differences in equivalent-width measurements affect completeness corrections, basically shifting a completeness curve
to higher or lower Wr . Since there is an offset in the relative equivalent-width “zero point” between studies (see
Appendix A), our equivalent-width limits are effectively
different and cause a shift in dNMg II /dX. For example,
the median deviation of Wr,ZM13 − Wr,S13 for matched
absorbers within ±1σW of Wr,2796 = 1 Å (where it matters most) is ≈ 0.01 Å to 0.02 Å but with large scatter
(median absolute deviation of ≈ 0.15 Å). If we compare
our dNMg II /dX values for Wr,2796 ≥ 1.1 Å to the ZM13
values for Wr,2796 ≥ 1 Å at z < 1.75, they agree exceedingly well.
P06 had Wr,2796 measurements that differed substantially from Q11, ZM13, and our values. Hence, the P06
suffer significantly from the relative Wr “zero point” issue. This effect, some unknown Malmquist bias, and,
most importantly, different completeness corrections lead
to P06 differing the most from our and other surveys.
Ultimately, the points of consensus for SDSS Mg II
systems are: f (Wr,2796 ) is well-modeled by an exponential; dNMg II /dX peaks at z ≈ 1.5; and the magnitude
of dNMg II /dX is largely consistent with the EDR results
(N05), with which Lundgren et al. (2009, partial DR5)
also agree.
4. DISCUSSION
Our Mg II catalog, in conjunction with the highredshift survey of Matejek & Simcoe (2012), traces the
cosmic chemical enrichment cycle from z2796 = 0.4 →
5.5, or from 10 Gyr to 1 Gyr after the Big Bang. Here
we examine how the evolution in dNMg II /dX relates to
galaxy evolution and how various absorber populations
evolve.
4.1. Mg II Evolution
Considering the direct evidence for strong Mg II systems arising in the gaseous halos of galaxies (e.g., Chen
et al. 2010a; Churchill et al. 2013), especially starforming ones (e.g., Martin & Bouché 2009; Rubin et al.
2013), we estimate the physical cross-section of Mg II absorbers, σphys , by assuming the co-moving number density of clouds equals ncom,B , the co-moving number density of B-band-selected galaxies, i.e.,:
dNMg II
c
=
ncom,B σphys .
dX
H0
(6)
These galaxies are bright, typically star-forming galaxies,
known to be associated with z . 2 Mg II absorbers (e.g.,
Martin & Bouché 2009; Rubin et al. 2013).
In Figure 8, we calculate ncom,B by integrating the Bband luminosity functions from Poli et al. (2003, crosses),
Gabasch et al. (2004, diamonds), Willmer et al. (2006,
squares), Marchesini et al. (2007, circles), and Cool
Evolution of Strong Mg II Absorbers
Age of Universe (Gyr)
3
2
1.3
0.15
0.10
Wr,2796 ≥ 1 Å
0.05
0.010
0.001
105
100
95
90
85
80
0.03
0.02
70
60
0.01
Cool et al. 2012
Gabasch et al. 2004
Marchesini et al. 2007
Poli et al. 2003
Willmer et al. 2006
0.00
0
1
2
3
Redshift
4
50
40
30
0
Rphys (kpc) = √ (σphys/π)
σphys (Mpc2) = H0/(cncom,B) dNMgII/dX
ncom,B (Mpc−3)
6
5
Figure 8. Mg II-absorbing halo cross-section estimate. Assuming
that all Wr,2796 ≥ 1 Å doublets are in B-band-selected galaxy halos
(with L ≥ 0.5 L∗ ), we estimated the galaxy-Mg II cross-section as
a function of z2796 (Equation 6). Top: We used dNMg II /dX from
the current study (blue plusses) and Matejek & Simcoe (2012, red
triangles). Middle: We calculated the co-moving number density of
galaxies by integrating the B-band luminosity functions from the
listed studies, down to 0.5 L∗ . The galaxies are bright, typically
star-forming galaxies, known to be associated with z . 2 Mg II absorbers (e.g., Martin & Bouché 2009; Rubin et al. 2013). Bottom:
The inferred cross-sections from the SDSS sample are comparable to observations (e.g., Chen et al. 2010a; Bordoloi et al. 2011;
Nielsen et al. 2013). The various studies providing the luminosity function parameters are linked by symbol across redshift and
by color between the middle and bottom panels. If possible, we
show multiple ncom,B and σphys per redshift, because the scatter between different studies characterizes the uncertainty in σphys
better than the estimated errors of any one survey.
et al. (2012, inverted triangles), down to 0.5 L∗ . At
z2796 < 2.3, where the cross-section uncertainties are
dominated by the ncom,B errors, σphys ≈ 0.005 Mpc2
to 0.015 Mpc2 . Assuming the Mg II-absorbing gas is distributed uniformly in a projected disk on the sky, the radius would be 40 kpc to 70 kpc (right-hand axis) for the
SDSS redshift range, which agrees well with the observed
radial profile of Mg II-absorbing galaxy halos (Chen et al.
2010a; Bordoloi et al. 2011; Nielsen et al. 2013, though
see Werk et al. 2013) and permits variation in the luminosity limit and/or covering fraction. The cross-section
is larger at higher redshifts, suggesting that L < 0.5 L∗
galaxies may contribute.
However, ultra-strong (Wr ≥ 3 Å) Mg II systems might
be associated with galaxy group gas (Gauthier 2013). If
we limit dNMg II /dX to 1 Å ≤ Wr < 3 Å systems, the
cross-sections is reduced by 5% to 10% from z = 0.4 to
2.3. Recent work by Werk et al. (2013) on the CGM of
z ≈ 0.2, L∗ galaxies showed that the covering fraction
for Wr,2796 ≥ 1 Å is small (. 30% within 50 kpc). It
is difficult to compare the SDSS systems with those of
Werk et al. (2013) because they have small statistics on
the Wr ≥ 1 Å absorbers.
Chen et al. (2010b) find a tighter correlation between
Wr,2796 and the projected distance to the host galaxy if
the latter is scaled by the B-band luminosity: Rgas =
75 × (LB /L∗ )0.35 h−1 kpc. If we adopt this model, we
can estimate the limiting luminosity, Llim , across redshift
that best reproduces the observed dNMg II /dX. Roughly,
Llim ≈ 0.015 L∗ at z2796 = 0.4 and increases to ≈ 0.1 L∗
at z2796 = 1.8 before dropping slightly in the last SDSS
redshift bin. This would increase ncom,B by up to a factor
of two, but both ncom,B and an estimated σphys would
evolve roughly as shown. The big caveat to applying
the Chen et al. (2010b) relation is that it was calibrated
at z2796 < 0.5, for Wr,2796 . 3 Å, and with L & 0.1 L∗
galaxies.
In Paper I, the C IV-absorbing cross-section was estimated to be roughly constant from z1548 ≈ 1.5 → 4.5,
assuming the co-moving density of clouds equals that
of UV-selected galaxies, and the evolution of ncom,UV
drives the approximately two-fold decrease of dNC IV /dX
in the redshift interval. In comparison, evolution in
dNMg II /dX might be driven by the (large) increase in
the Mg II-absorbing cross-section of galaxies from lowto-high redshift (Figure 8). Though, the evolution might
be a result of a changing population of galaxies (e.g.,
L < 0.5 L∗ ) that host Mg II absorbers. We will explore
these scenarios in a future paper.
13
1.00
Age of Universe (Gyr)
3
2
6
1.3
1
0.9
HI τ ≥ 2
DLA logNHI ≥ 20.3
MgII 0.3 Å ≤ Wr < 1 Å
MgII Wr ≥ 1 Å
CIV Wr ≥ 0.6 Å
dNion/dX
dNMgII/dX
13
0.20
11
0.10
0.01
0
1
2
3
Redshift
4
5
6
Figure 9. Line density evolution of various absorber populations:
τ > 2 H I systems (i.e., LLS and DLA; gray); DLAs only (black);
strong Mg II and C IV systems (blue and red, respectively); and
weaker Mg II systems at high redshift (cyan) from the following
studies: H I—Fumagalli et al. (2013, circles); DLA—Rao et al.
(2006, diamonds), Prochaska & Wolfe (2009, filled squares), Noterdaeme et al. (2012, squares); Mg II—current work (plusses),
Matejek & Simcoe (2012, triangles); and C IV—Cooksey et al.
(2010, filled circle), Paper I (plusses), Simcoe et al. (2011, crosses).
4.2. Evolution of Various Absorber Populations
12
Seyffert et al.
Most, if not all, SDSS Mg II systems have other metal
lines and, where coverage exists, H I absorption. These
associated transitions assisted our visual verification, and
in their automated procedure, ZM13 used detection of
(probable) Fe II lines to disentangle Mg II doublets from
other possible identifications. In addition to transitions
of H I Lyman series and iron, Mg II systems can have aluminium, silicon, and/or carbon absorption. Here we examine dNion /dX of various samples, selected on the basis of different transitions—DLAs, Lyman-limit systems
(LLSs), strong C IV, and strong and weaker Mg II—
and discuss the evolution of these common tracers of the
CGM and IGM across cosmic time (Figure 9).
The differently evolving absorbers in Figure 9 could
be physically explained, independently, as follows: (i)
optical depth τ ≥ 2 H I systems decrease with time
as the universe becomes more ionized; (ii) strong C IV
systems increase with the increasing metallicity of the
universe; (iii) strong Mg II systems evolve with time in
lock-step with ρ∗ ; and (iv) weaker Mg II systems are established early or constantly replenished so as to evolve
little. Though these explanations may be partially or
completely true, they neither consider nor shed light on
the evolution of the other ions. We attempt to describe
the evolution of common QAL systems holistically.
We postulate that each ion has multiple subpopulations, which together, yield the observed
dNion /dX. A difficulty arises in how to fairly compare the data, considering the varying equivalent-width,
column-density, or optical-depth limits. For this discussion, we simply compile the best published values
for a given cutoff. For τ ≥ 2 H I systems (i.e., LLSs
and DLAs), we use the compilation by Fumagalli et al.
(2013), which is based on their measurement at z = 2.8
and Ribaudo et al. (2011, values centered at z < 1.5),
O’Meara et al. (2013, 1.5 < z < 3), and Prochaska
et al. (2010, z > 3.5). The DLA-only dN /dX values
are from Rao et al. (2006, z < 2), Noterdaeme et al.
(2012, 2 < z < 3.5), and Prochaska & Wolfe (2009,
2 < z < 5.5). The current work and Matejek & Simcoe
(2012, z > 2) provide dNMg II /dX for Wr,2796 ≥ 1 Å, and
the line densities for 0.3 Å ≤ Wr,2796 < 1 Å absorbers
are from the latter survey. For Wr,1548 ≥ 0.6 Å C IV
systems, we use Cooksey et al. (2010, z < 1), Paper I
(1.5 < z < 4.5), and Simcoe et al. (2011, z > 4.5).
In the original SDSS Mg II paper, N05 discussed “multiple Mg II” populations. They noted that DLAs, possible disks of star-forming galaxies, are a fraction of strong
Mg II systems and that bright, spiral galaxies are not
guaranteed to be found near all strong Mg II absorbers,
statistically. Rao et al. (2006) estimated that ≈ 35%–
40% of Mg II systems with Wr,2796 ≥ 0.5 Å and a few
other constraints (Fe II λ2600 and Mg I λ2852 absorption, doublet ratio) were DLAs at z < 1.65.
The fraction of Wr,2796 ≥ 1 Å Mg II systems exhibiting dampled Lyα absorption16 is consistent with the observed ≈ 35%–40%, over the same redshift range. Overall, the fraction grows from low-to-high redshift, becom16 We estimate the number of absorbers by assuming we would
find Nion = (dNion /dX)∆X in a given survey path length ∆X.
Thus, we approximate the fraction of e.g., non-DLA Mg II systems
to C IV systems as (dNMg II /dX − dNDLA /dX)/(dNC IV /dX).
ing greater than unity at z ≈ 4, but the ratio of DLAs
to 0.3 Å ≤ Wr,2796 < 1 Å Mg II systems, though also
growing, stays below 100%. Matejek & Simcoe (2012)
and ZM13 show that dNMg II /dX for these weaker systems is roughly constant from z = 0.4 → 5.5. Thus, the
equivalent-width limit of the DLA-tracing Mg II population may evolve with redshift.
Churchill et al. (2000) proposed a Mg II taxonomy: Classic, Single/Weak, C IV-Deficient, Double, and
DLA/H I-rich. They identified these classes from nonparametric clustering analysis of 30 Mg II systems with
measured equivalent widths of Lyα, Mg II, Fe II (or limits), and C IV (or limits). Their sample came from 45
0.4 < z < 1.4 Mg II systems with high-resolution optical
and low-resolution UV spectroscopy and had Wr,2796 <
1.8 Å, and Wr,1548 < 2 Å. The Classic and Double Mg II
absorbers—30% and 10%, respectively, of the 30—are
C IV strong, with the latter having the largest Wr,1548
and Wr,2796 , possibly because they are two, close Classic
systems. Single/Weak systems (23%) are C IV-weak but
not remiss of absorption like the C IV-Deficient group
(20%). The DLA/H I-rich class comprise the remaining
17% and have the largest Wr,2796 but Wr,1548 is comparable to the Single/Weak population.
The fraction of strong Mg II systems, not in DLAs, relative to C IV systems grows from ≈ 10% at low redshift
to roughly 40% at z ≈ 3, before decreasing sharply. For
the overlapping redshift range, this is consistent with the
Churchill et al. (2000) sample, if they were to define a
“strong Mg II and C IV but not DLA” class. The steep
z > 3 decline is due to non-DLA, strong Mg II systems
vanishing, possibly, as the weaker Mg II systems encompass a significant DLA population.
However, the ratio of non-DLA Mg II absorbers to nonDLA H I systems (i.e., LLSs) roughly decreases from
≈ 50% at z = 1 to zero at z = 4, though the rate of
decline is steeper at z & 2 to 3. The steeper decline could
be due to there being less strong Mg II systems after the
ρ∗ peak, as discussed previously, or because there is an
increasing LLS sub-population due to the (metal-poor)
IGM at high redshift (Fumagalli et al. 2013).
We are not able to disentangle a C IV-Deficient,
(strong) Mg II population at any redshift because
dNC IV /dX (Wr,1548 ≥ 0.6 Å) is larger than dNMg II /dX
(Wr,2796 ≥ 1 Å) at all redshifts. However, in the
Churchill et al. (2000) sample, one-half to one-third of
the Single/Weak class have SDSS-strength C IV absorption, which is roughly 10% of their entire sample. The
shape of the C IV f (Wr ) does not evolve significantly
over z = 1.5 → 4.5 (Paper I); instead, the overall normalization changes smoothly, driving the evolution in
dNC IV /dX. Thus, the sub-populations comprising the
Wr,1548 ≥ 0.6 Å systems must evolve smoothly or “conspiratorially” to preserve the shape of f (Wr,1548 ).
Fundamentally, the number of observed systems and
their associated ions are determined by: elemental abundances; strength and shape of the ionizing radiation; and
the spatial distribution (e.g., density, cross-section) of
the gas. The complex physics involved make cosmological simulations, if they resolve enrichment processes in
the CGM and IGM, a powerful tool in understanding the
evolution of various absorber populations in tandem. On
the flip side, results from QAL studies are top-level con-
Evolution of Strong Mg II Absorbers
straints on ongoing and cumulative enrichment processes
and should be leveraged to assess whether cosmological
simulations reproduce reality. From the observational
plane, we will revisit the issue of the evolution of various
absorber populations in a future paper.
5. SUMMARY
We have conducted a survey for Mg II systems in
79,294 SDSS DR7 quasar spectra (Schneider et al. 2010);
these were chosen because they were not BAL QSOs and
had median hS/Ni ≥ 4 pixel−1 in the region covering
intergalactic Mg II absorption. Candidate Mg II doublets were automatically detected, and the final catalog
was visually verified. This resulted in 34,254 doublets
with δvQSO < −5000 km s−1 and outside the quasar C IV
emission region, used for further analyses; the full catalog
and other tools for analysis (e.g., completeness grids) are
made available for the community.17 Our Monte-Carlo
completeness tests included the effects of the automated
algorithms and user bias (e.g., the accepted false-positive
rate).
Though there exist differences in methodologies, from
continuum fitting to final doublet selection, we recovered
over 76% of the P06 absorbers, 80% of Q11, and 72% of
ZM13. We also detect systems not in these other SDSS
catalogs.
We analyzed the catalog as a whole and in 14 small
redshift bins with roughly 2500 doublets each. The
equivalent-width frequency distribution is described well
by an exponential model for all redshifts. It flattens
with increasing redshift, indicating there are more strong
absorbers relative to weaker ones. Moreover, the bestfit parameters evolve relatively smoothly from low-tointermediate redshift.
We compare dNMg II /dX for a range of limiting equivalent widths and find significant differential evolution
with Wr,lim . Namely, the stronger Mg II systems evolve
more with redshift, as predicted by the changing shape
of f (Wr ) over time. In addition, the peak in dNMg II /dX
appears to be at higher redshift for larger Wr,lim .
All SDSS studies detect the dNMg II /dz increase and
a peak between z ≈ 1.5 to 2.3. On the other hand, we
do not measure a decrease in the characteristic equivalent width, W ∗ , at z2796 > 1.75 seen in ZM13. However,
it is difficult to disentangle the degeneracy between W ∗
and N ∗ (i.e., α and k). Additionally, the dNMg II /dX
measurements differ by up to 50% due to differences in
methodologies, and we discussed the effects of Malmquist
bias and offsets in rest equivalent-width measurements.
The bias arises from more absorbers scattering above
Wr,lim than below, due to measurement uncertainties.
A small change in in the relative Wr,2796 “zero point”
has a significant impact on the absorber line density. Of
course, differences in completeness corrections can contribute greatly to differences in survey results.
Assuming the co-moving number density of Mg IIabsorbing clouds equals the co-moving number density
of B-band-selected galaxies with L ≥ 0.5 L∗ , the physical cross-section of the galaxies is estimated to grow
from σphys ≈ 0.005 Mpc2 to 0.015 Mpc2 over z = 0.4 →
2.3. The increase in σphys might drive the increase in
17
See http://igmabsorbers.info/.
13
dNMg II /dX, but the evolution in the line density might
reflect a changing population of Mg II-absorbing galaxies. We also explored the effect of cross-section scaling
with the galaxy B-band luminosity and with dNMg II /dX
for 1 Å ≤ Wr < 3 Å systems, which are more likely individual galaxy halos as opposed to intra-group gas.
A holistic approach is taken in discussing the evolution
of various absorber population, where we assume that
each ion has multiple sub-populations yielding the observed dNion /dX. The intersection of DLAs and strong
Mg II absorbers grows from low-to-high redshift, but
weaker (0.3 Å ≤ Wr,2796 < 1 Å) Mg II systems may better trace the DLAs at z & 3. The population of strong,
non-DLA-tracing Mg II and strong C IV system grows
from low-to-high redshift, before decreasing sharply at
z ≈ 3. Finally the fraction of non-DLA Mg II absorbers
in LLSs decreases from 50% to zero over z = 1 → 4.
This is the second paper in our Precious Metals in
SDSS Quasar Spectra project. Early versions of this catalog have already been used to compare Mg II system
properties across redshift (Matejek et al. 2013) and for
Mg II-galaxy clustering analysis (Gauthier et al. 2013).
Future Precious Metals studies include modeling Mg IIabsorbing cross-sections, a fairly comparable Si IV catalog, and multi-ion classification analysis.
The current study was funded largely by the National
Science Foundation Astronomy & Astrophysics Postdoctoral Fellowship (AST-1003139) and in part by MIT
Undergraduate Research Opportunity Program (UROP)
Direct Funding, from the Office of Undergraduate Advising and Academic Programming and the John Reed
UROP Fund. RAS acknowledges support from NSF
grants AST-0908920 and AST-1109915, and JXP acknowledges support from NSF AST-0709235 and AST1010004.
We appreciate J.-R. Gauthier and H.-W. Chen’s help
in making our catalog better. We thank M. Sinha for his
programming help and P. Jonsson for productive discussions regarding statistics and programming. We gratefully acknowledge the vital role and last huzzah (for us)
of the Adam J. Burgasser Endowed Chair.
Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site
is http://www.sdss.org/.
The SDSS is managed by the Astrophysical Research
Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western
Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the
Japan Participation Group, Johns Hopkins University,
the Joint Institute for Nuclear Astrophysics, the Kavli
Institute for Particle Astrophysics and Cosmology, the
Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the
Max-Planck-Institute for Astronomy (MPIA), the Max-
14
Seyffert et al.
Planck-Institute for Astrophysics (MPA), New Mexico
State University, Ohio State University, University of
Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the
University of Washington.
Facilities: Sloan
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APPENDIX
DETAILED COMPARISON WITH PREVIOUS SDSS MG II CATALOGS
In Section 2.3, we summarized the differences between four previous Mg II surveys, that used the following SDSS
data releases: early (Nestor et al. 2005); third (Prochter et al. 2006a); fourth (Quider et al. 2011); and seventh (Zhu
& Ménard 2013).8 Here we provide specific absorber-to-absorber details.
N05 surveyed approximately 3700 zQSO ≥ 0.37 sightlines in the SDSS EDR quasar catalog (Schneider et al. 2002)
and visually verified 1331 Mg II doublets with 0.3 Å ≤ Wr,2796 < 5.7 Å and 0.36 < z2796 < 2.27. In DR7, there remains
3809 of the 3814 total QSOs in EDR, and in those, we detect 1425 absorbers with Wr,2796 . 9 Å with the same redshift
range. N05 did not publish their line catalog, but it was folded in to the DR4 survey of Q11, which is discussed below.
P06 surveyed 45,023 zQSO > 0.35 quasar spectra in the DR3 quasar catalog (Schneider et al. 2005) and published a
catalog of the resulting, visually verified 7410 doublets, with 1 Å ≤ Wr,2796 ≤ 10.1 Å and 0.36 < z2796 ≤ 2.28. There
0.8
Number (103)
15
1.5
Seyffert et al. (2013)
Quider et al. (2011)
Number (103)
Seyffert et al. (2013)
Prochter et al. (2006)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
14
12
10
8
6
4
2
0
0.6
0.4
0.2
0.0
1.0
0.5
15
10
5
1.0
1.5
2.0
2.5
Total
Unique
30
20
10
0
0.5
Seyffert et al. (2013)
Zhu & Menard (2013)
0.0
Total
Unique
Cumulative (103)
Total
Unique
Cumulative (103)
Cumulative (103)
Number (103)
Evolution of Strong Mg II Absorbers
0
0.5
z2796
1.0
1.5
2.0
2.5
0.5
z2796
1.0
1.5
z2796
2.0
2.5
Figure 10. Comparing redshift distributions of published SDSS Mg II catalogs: P06 (DR3, left); Q11 (DR4, middle); and ZM13 (DR7,
right). The solid histograms show each catalog’s full distribution (for the same data release), while the dashed histograms are each catalog’s
unique sample (our current catalog in black, others in red). The hard Wr,2796 ≥ 1 Å limit in P06 (Figure 11) drives the differences in the
catalogs. For Q11 and ZM13, the systems unique to the current study tend to be at lower redshift (black, dashed histograms).
6
5
5
4
4
3
3
2
2
1
6
6
4
4
2
2
Wr,2796 (Å) [ZM13]
6
Wr,2796 (Å) [Q11]
Wr,2796 (Å) [P06]
are 44,545 DR3 sightlines in the DR7 catalog, and we identified 15,083 Mg II systems. In Figures 10 and 11, we
compare z2796 and Wr,2796 for the intersection of the P06 and our catalogs (5693 doublets) and for the systems unique
to either (1717 and 9390, respectively). The P06-only systems are generally spread out in redshift (Figure 10). P06
measured equivalent widths by summing the flux absorbed in 3589 Å boxes, centered at the redshift of the 2796 Å
line. As can be seen in Figure 11, this and a systematically low continuum fit results in an underestimation of the
equivalent width for strong systems.
We do not recover the 1717 doublets unique to P06 for the following reasons (number): in Shen et al. (2011) BAL
QSO sightlines (730); (S/N)conv < 2.5 resel−1 in the 2803 Å line in our normalized spectra (588); in sightlines with
hS/Ni < 4 pixel−1 (296); (S/N)conv < 3.5 resel−1 in the 2796 Å line in our normalized spectra (65); in visual BAL QSO
sightlines (35); and within 3000 km s−1 of the Schneider et al. (2010) quasar redshift (3). Of the 9393 doublets unique
to our catalog, 6787 (72%) have Wr,2796 < 1 Å, which Prochter et al. (2006a) excluded by construction.
6
6
4
4
2
2
1
y=x
y = 0.039 Å + 0.864 x
Histogram: Total
Unique
0
0
2
4
Wr,2796 (Å) [S13]
6
0
y=x
y = 0.072 Å + 0.960 x
Histogram: Total
Unique
0
0
2
4
Wr,2796 (Å) [S13]
6
0
0
y=x
y = 0.033 Å + 0.972 x
Histogram: Total
Unique
0
2
4
Wr,2796 (Å) [S13]
6
Figure 11. Comparing rest equivalent-width distributions of published SDSS Mg II catalogs. For all catalogs, the unique systems tend
to be the weaker systems (red histograms). P06 only published systems with Wr ≥ 1 Å (left). They also had the largest discrepancy with
our measured equivalent widths. The green, dashed lines show the one-to-one relation. The orange, dash-dot lines are linear least-squares
fits, including errors in both datasets, with three-sigma errors (orange, dotted lines). The black histograms show the redshift distribution
of the matched systems from each catalog.
Q11 surveyed 44,620 zQSO > 0.36 quasar sightlines in the SDSS DR4 database, and they give the details of their
SQL query. They visually verified 17,042 Mg II systems with 0.15 Å < Wr,2796 < 6.5 Å and 0.36 < z2796 < 2.29. In
DR7, there remains 44,463 of the DR4 quasars, in which we detect 18,188 systems. The intersection of our catalogs
0
16
Seyffert et al.
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
y=x
y = 0.191 + 0.857 x
Histogram: Total
Unique
0
0
1
2
3
Wr,2796/Wr,2803 [S13]
0
4
Wr,2796/Wr,2803 [ZM13]
Wr,2796/Wr,2803 [Q11]
yields 13,783 systems, leaving 3258 doublets unique to Q11 and 4405 to us; Figures 10, 11, and 12 show the z2796 ,
Wr,2796 , and Wr,2796 /Wr,2803 distributions for matched and unique samples. There is an excess of our unique Mg II
systems, at low redshift. Our Wr,2796 measurements agreed well, even though Q11 used Gaussian fits and we used
boxcar summation, and systems unique to either catalog tend to cluster at Wr,2796 < 1 Å. There is a significant tilt
when comparing our equivalent-width ratios, and our unique systems tend to have ratios less than unity, which mean
they have blended 2803 Å lines.
We do not recover 3260 systems unique to Q11 for the following reasons (number): in BAL QSO sightlines (1617);
(S/N)conv < 2.5 resel−1 in the 2803 Å line (1172) and (S/N)conv < 3.5 resel−1 in the 2796 Å line (294) in our normalized
spectra; in visual BAL QSO sightlines (94); in sightlines with hS/Ni < 4 pixel−1 (79); and in sightlines no longer in
DR7 (4). Of the 4403 doublets unique to our catalog, 3092 (70%) have Wr,2796 < 1 Å.
ZM13 surveyed a total of 84,533 DR7 quasar spectra, 569 from Hewett & Wild (2010) and the rest from Schneider
et al. (2010). For all quasars, ZM13 adopted the Hewett & Wild (2010) quasar redshifts. ZM13 conducted a completely
automated search, using Q11 as a training set, and identified 35,752 systems with Wr,2796 < 8.5 Å and 0.36 < z2796 <
2.29. Comparing our full catalog of 35,629 Mg II systems, both catalogs agree on 25,909 systems, leaving 9843 systems
unique to ZM13 and 9720 to us. We show the z2796 , Wr,2796 , and Wr,2796 /Wr,2803 distributions for the matched and
unique samples in Figures 10, 11, and 12. There is a strong trend for our unique doublets to be at low redshift, since
ZM13 did not search the C IV “forest,” requiring ∆z > 0.02 red-ward of the quasar C IV emission line. Our Wr,2796
values agree well; ZM13 also measured the equivalent width from Gaussian fits. The doublets unique to either catalog
peak at Wr,2796 < 1 Å. There is a significant tilt in the equivalent-width-ratio plane, and our unique systems are
relatively evenly distributed around a ratio of unity.
We do not recover 9843 systems unique to ZM13 for the following reasons (number): (S/N)conv < 2.5 resel−1 in the
2803 Å line in our normalized spectra (5193); in BAL QSO sightlines (3075); (S/N)conv < 3.5 resel−1 in the 2796 Å
line in our normalized spectra (976); in sightlines with hS/Ni < 4 pixel−1 (291); in visual BAL QSO sightlines (209);
and in Hewett & Wild (2010) sightlines (99). Of the 9720 doublets unique to our catalog, 3387 were not recovered by
ZM13 because they are in the C IV forest; 793 because they are within ∆z = 0.04 of the Hewett & Wild (2010) quasar
Mg II emission line; and 156 because they are coincident with Galactic Ca II λλ3934, 3969.
y=x
y = 0.382 + 0.662 x
Histogram: Total
Unique
0
0
1
2
3
Wr,2796/Wr,2803 [S13]
0
4
Figure 12. Comparing rest equivalent-width ratio distributions of published SDSS Mg II catalogs; the colored lines and histograms are
similar to those described in Figure 11. (P06 did not published the equivalent widths of the Mg II 2803 Å line.) Though the equivalent
widths for matched systems were largely in agreement (Figure 11), the ratios show larger disagreement (orange, dashed lines). The systems
unique to Q11 and ZM13 tend to be less saturated systems (ratios > 1; red histograms, vertical axes). Since the unique systems from all
catalogs were largely lower-Wr,2796 systems, it appears Q11 and ZM13 were more sensitive to weak Wr,2796 doublets with weaker Wr,2803
lines, while we picked up on weak, saturated and/or blended systems, where blending can drive the ratio below unity.